# GNSS Principles

## Basic Principle of GNSS

The basis of all GNSS systems is that a user determines it position by measuring to at least 4 GNSS satellites at the same time. These measurements give the user 4 distance measurements between himself and the 4 satellites. With four measurements one can resolve 4 unknowns. For the end user these 4 unknowns are the 3 unknowns of his position (X, Y, and Z or Latitude, Longitude, and Height) and the clock error of his GNSS receiver.

## GNSS and Time

So why do we need to estimate the clock error of our GNSS reciever!? Well, the measurements that are made by GNSS receivers are not distance measurements. GNSS receivers measure the amount of time it took the signal to travel from the satellite to the receiver, i.e., the travel time. However, to measure this travel time the receiver has to know the time the signal left the satellite as well as the time the signal arrived at the receiver. When leaving the satellite the signal gets a time-tag. In that way the receiver knows the exact time of transmission of the signal. To know the exact time of arrival the receiver needs to know its own time very accurately. The most economical way to realise this is by using a very cheap clock inside the receiver. Typically a quartz clock (oscilator) similar to the one in your wrist watch or computer. This time will, however, not be accurate enough and therefore the receiver has to compute the clock error of its own (cheap) clock.

The measured travel time is multiplied with the signal travel speed to get the actual distance between the satellite and the receiver. The signal travel speed is the speed of light, i.e., 300 km/s, at least in the vacuum of space, a bit slower in the Earths atmosphere. So in order to have a measurement accuracy of a few meters the satellite and receiver time will have to be know with an accuracy of around 10 microseconds. This implies that the satellites need to be able to keep time at this 10 microseconds level!! This timing accuracy can only be achieved by using atomic clocks. And since time keeping is one of the most essential elements of a GNSS satellite they actually carry several atomic clock for redundancy. In addition the ground segment monitors the clock behavior and in addtion to time stamping the signals the satellites also broadcast information regarding the offset, rate, and rate-rate of their on-board clock.

Due to the importance of accurate timeing the European GNSS Galileo is planning to use very advanced clocks called Hydrogen masers. This is one of the unique features of the Galileo system. The GIOVE-B satellite is flying a H-Maser as proof of concept and to make it "space proven". The GPS system evolutions, Block-IIF and Block-III, do unfortunately not plan to use such advanced clocks. The expected (big) advantage of the H-Maser is that its behaviour can be predicted much more accurately over time spans of several hours.

Since the receiver has to compute the error of its own clock it actually get to tell time at an amazing level of accuracy. So a GNSS based clock would be something really accurate! In fact there are some GPS wrist watches on the market today be because of power consumtion they are rather bulky. Nevertheless, timing is one of the fiels in which GPS is used very much. Any application in need of accurate timing is using a GPS receiver. Examples are time keeping of computer systems, time stamping of bank transactions (very important!), communication systems, and in fact most likely the time your computer in the office runs on is based on GPS.

## GNSS Measurement Corrections

So, now we have 4 distance measurements and we know they all end at the same point, namely the location of the receiver. However, in order to be able to compute this location we actually need to know from where these distance measurements originated. Clearly, they originated from the GNSS satellites. So besides informing our receiver about their clock errors the satellites also have to inform us about their current position. All this information, satellite position and clock biases, and more, are contained in what is referred to as the satellite broadcast ephemerides. This is data which is incorporated in the actual measurment streams.

With the 4 distance measurements and the satellite positions we can now easily determine the location of our receiver and its clock offset. This position estimate will, however, be limited in accuracy since there are a couple of measurement corrections we should apply. The GNSS signal travel with the speed of light as long as they are in the vacuum of space. In the Earths atmosphere the signals get disturbed. Firstly, in the ionospere, the upper layer of the Earths atmosphere (~above 50km). Secondly, in the troposphere, the lower 50km of the Earth's atmosphere.

The effect of the ionosphere may be correct by using signals on two frequencies. This is why all GNSS systems transmit on at least two frequencies. Unfortunately, currently with GPS the second frequency is meant for military usage. So for our simple car navigation units we will have to use a model for the Ionosphere to correct for the main effect of it on our single frequency measurements. In fact, the broadcast navigation message, which gave us the satelite position and the clock errors, also gives us a model for the ionosphere, called Klobuchar model. The ionospheric delays on the signal are of the order of tens of meters. With the Klobuchar model the ionospheric effects can be modeled with meter level precision.

The tropospheric effect can also be accounted for by using a model. For a measurement in zenith (straight up) the tropospheric delay is of the order of 2 meters. For low elevation measurements this effect grows to the level of 10 meters due to the longer time the signal has to travels through the tropospere. The main unknown in the tropospheric delay is the amount of water vapour in the air. However, with a relatively simple model the effect of the troposphere can be modeled at the sub-meter level.

## GNSS Position Estimate

So we have 4 measurments with an accuracy of about 1 meter. We can model these measurments with a few meter level accuracy. Thus we are able to compute our position with a few meter accuracy. And that is what GNSS offers you at anytime, anywhere, on our lovely planet! Great for finding your way irrespective if you are walking, driving, sailing, or even flying!